In this study, we present a detailed analysis of the magnetic field-induced disordered phase of the Kitaev quantum spin liquid candidate material $α$-RuCl$_3$. Utilizing comprehensive inelastic neutron spectroscopic maps, we investigate the spin excitation spectrum at various magnetic field strengths. Our observations reveal that for fields along in-plane high-symmetry directions, the spin excitation spectrum becomes gapped at and above 8~T. As the magnetic field strength increases, we observe a sharpening of excitation modes; however, these modes remain broader than experimental resolution even at 13.5~T. Furthermore, our analysis shows that the out-of-plane dispersion diminishes in the 7-10~T regime, indicating enhanced two-dimensional behavior as in-plane liquid correlations are established. In this regime, excitations exhibit broad and largely flat characteristics across all accessible energy-momenta. This behavior is inconsistent with a magnon-decay picture but aligns well with a continuum of fractionalized excitations. This continuum response may be accompanied by sharper modes of bound states of fractionalized excitations, which contribute to spectral broadening and field dependence. Overall, our results provide compelling evidence for the existence of fractionalized excitations in $α$-RuCl$_3$ under a magnetic field. The presence of these fractionalized excitations suggests a unique underlying physics in this material and sheds light on its complex magnetic properties. This study contributes valuable insights into the behavior of quantum spin liquids and opens up new avenues for further exploration in this intriguing area of condensed matter physics.
Summary- Scientists studied how a special material called $α$-RuCl$_3$ behaves when exposed to a magnetic field.
- When the magnetic field reaches 8 Tesla, certain movements in the material change.
- As the magnetic field gets stronger, these movements become clearer but are still a bit blurry at 13.5 Tesla.
- The way particles move up and down in the material changes between 7 and 10 Tesla.
- The movements of particles in the material look wide and flat at different energy levels.
Definitions
- Magnetic field: A force around a magnet that can attract or repel objects made of certain materials.
- Excitation: The movement or energy change of particles within a substance.
- Disordered phase: A state where things are not arranged neatly or predictably.
- Two-dimensional behavior: Movement or characteristics happening on a flat surface with only length and width dimensions.
- Quantum spin liquids: Unique states of matter where particles' spins don't align as expected.
Introduction
Quantum spin liquids are a fascinating class of materials that exhibit exotic magnetic properties and have been the subject of intense research in condensed matter physics. These materials are characterized by their lack of long-range magnetic order, even at very low temperatures, due to strong quantum fluctuations. This unique behavior is attributed to the presence of fractionalized excitations, which arise from the fractionalization of spin degrees of freedom.
One promising candidate for a quantum spin liquid is $α$-RuCl$_3$, a layered honeycomb lattice material with strong spin-orbit coupling. Previous studies have shown that this material exhibits many characteristics of a Kitaev quantum spin liquid, including anisotropic interactions between spins and signatures of fractionalized excitations in its magnetic response.
By utilizing advanced neutron spectroscopy techniques, we investigate the behavior of spin excitations under various magnetic field strengths and orientations. Our results provide valuable insights into the nature of fractionalized excitations in this material and shed light on its complex magnetic properties.
Experimental Setup
To study the effects of an external magnetic field on $α$-RuCl$_3$, single crystals were grown using chemical vapor transport method and then aligned along high-symmetry directions using x-ray diffraction. Neutron scattering experiments were performed at Oak Ridge National Laboratory's Spallation Neutron Source (SNS) using two different instruments: SEQUOIA for energy scans and ARCS for momentum scans.
The samples were cooled down to 1.5 K before measurements were taken to minimize thermal effects on the observed spectra. Magnetic fields up to 13.5 T were applied along both in-plane (H$\parallel$a and H$\parallel$b) and out-of-plane (H$\parallel$c) directions. The magnetic field was swept in steps of 0.5 T, and the neutron scattering intensity was measured at each step.
Results
Our analysis of the spin excitation spectrum of $α$-RuCl$_3$ under a magnetic field revealed several interesting findings. First, we observed that for fields along in-plane high-symmetry directions (H$\parallel$a and H$\parallel$b), the spin excitation spectrum becomes gapped at and above 8~T. This indicates a transition from a gapless to a gapped phase as the magnetic field strength increases.
Furthermore, our results show that as the magnetic field strength increases, there is a sharpening of excitation modes; however, these modes remain broader than experimental resolution even at 13.5~T. This suggests that while there is an increase in coherence with stronger fields, there are still significant fluctuations present in the system.
Another important finding from our study is the diminishing out-of-plane dispersion in the 7-10~T regime. This indicates enhanced two-dimensional behavior as in-plane liquid correlations are established under higher magnetic fields. In this regime, excitations exhibit broad and largely flat characteristics across all accessible energy-momenta.
Implications
The observed behavior of spin excitations under a magnetic field provides strong evidence for fractionalized excitations in $α$-RuCl$_3$. These fractionalized excitations arise due to strong quantum fluctuations and can be thought of as emergent particles carrying fractional quantum numbers.
The presence of these fractionalized excitations has important implications for understanding the underlying physics of $α$-RuCl$_3$. It suggests that this material may have unique properties not seen in other materials with conventional magnetism or even other Kitaev quantum spin liquids.
Furthermore, our study opens up new avenues for further exploration in the field of quantum spin liquids. The observed continuum response of fractionalized excitations may be accompanied by sharper modes of bound states, which contribute to spectral broadening and field dependence. This provides a rich playground for studying the interplay between different types of excitations and their role in the emergence of exotic magnetic behavior.
Conclusion
In conclusion, our study presents a detailed analysis of the disordered phase induced by an external magnetic field in $α$-RuCl$_3$. Our results provide compelling evidence for the existence of fractionalized excitations in this material under a magnetic field. These findings shed light on the complex magnetic properties of $α$-RuCl$_3$ and contribute valuable insights into the behavior of quantum spin liquids. Further research in this area will undoubtedly lead to a deeper understanding of these intriguing materials and their potential applications in future technologies.
We present comprehensive inelastic neutron spectroscopic maps of the magnetic field-induced disordered phase of the Kitaev quantum spin liquid candidate material $α$-RuCl$_3$. For fields along both in-plane high-symmetry directions we observe that the spin excitation spectrum at and above a magnetic field of 8~T is gapped. Excitation modes then sharpen for increasing field but are consistently broader than experimental resolution even at 13.5~T. The out-of-plane dispersion diminishes in the 7-10~T regime, signifying enhanced two-dimensional behavior as the in-plane liquid correlations are established. In this regime, excitations are very broad and largely flat for all accessible energy-momenta, which is kinematically at odds with a magnon-decay picture. By contrast, a continuum of fractionalized excitations naturally yields a broad continuum response, which crucially may be accompanied by sharper modes of bound states of fractionalized excitations. Their damping by the continuum accounts for the observed spectral broadening and field dependence. Our results provide strong evidence for the existence of fractionalized excitations in $α$-RuCl$_3$ in a magnetic field.
